Electron beam exposure method using variable backward scattering coefficient and computer-readable recording medium having thereof

Abstract

An electron beam exposure method is disclosed. First, An exposure region is divided into a plurality of grating regions. A pattern density is obtained for one of the plurality of grating regions. A backward scattering coefficient is determined in accordance with the pattern density for the one of the plurality of grating regions. An exposure dose amount is calculated from the backward scattering coefficient. The one of the plurality of grating regions is exposed with the calculated exposure dose amount. The backward scattering coefficient is provided with a variable function proportional to the pattern density. The backward scattering coefficient eta is provided with a variable value depending on the pattern density and location of the one of the plurality of grating regions.

What is claimed is:  
     
       1. An electron beam exposure method, comprising the steps of: 
       dividing an exposure region into a plurality of grating regions;  
       obtaining a pattern density for one of the plurality of grating regions;  
       determining a backward scattering coefficient in accordance with the pattern density for the one of the plurality of grating regions;  
       calculating an exposure dose amount from the backward scattering coefficient; and  
       exposing the one of the plurality of grating regions with the calculated exposure dose amount.  
     
     
       2. The electron beam exposure method of  claim 1 , wherein the backward scattering coefficient is provided with a variable function proportional to the pattern density. 
     
     
       3. The electron beam exposure method of  claim 1 , wherein the backward scattering coefficient is provided with a variable value depending on the pattern density and location of the one of the plurality of grating regions. 
     
     
       4. The electron beam exposure method of  claim 1 , wherein the plurality of grating regions comprise a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region and a second backward scattering coefficient, wherein the second backward scattering coefficient is higher than the first backward scattering coefficient. 
     
     
       5. An electron beam exposure method, comprising the steps of: 
       dividing an exposure region into a plurality of grating regions;  
       obtaining respective pattern densities for the plurality of grating regions;  
       generating a pattern map with locations of the exposure region in accordance with the pattern densities in the respective plurality of grating regions;  
       determining backward scattering coefficients for the plurality of grating regions in accordance with the respective pattern densities and the locations of the exposure region;  
       generating a backward scattering coefficient map with the locations of the exposure region in accordance with the backward scattering coefficients;  
       calculating an exposure dose amount for the plurality of grating regions in accordance with the backward scattering coefficients obtained from the backward scattering coefficient map; and  
       exposing the plurality of grating regions with the calculated exposure dose amount.  
     
     
       6. The electron beam exposure method of  claim 5 , wherein the backward scattering coefficients are provided with a variable function proportional to the pattern densities. 
     
     
       7. The electron beam exposure method of  claim 5 , wherein the backward scattering coefficients are provided with variable values depending on the pattern densities and the locations of the grating regions. 
     
     
       8. The electron beam exposure method of  claim 5 , wherein the plurality of grating regions comprise a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the pattern region and a second backward scattering coefficient, wherein the second backward scattering coefficient is higher than the first backward scattering coefficient of the first grating region. 
     
     
       9. The electron beam exposure method of  claim 5 , wherein the step of the calculating the exposure dose amount comprises the following equation:          D        (     d   r     )       =         1   +     2                 η         1   +     2        d   r        η         ·     D        (   1   )                         
       wherein D(d r ) is the exposure dose amount, η is the backward scattering coefficient, d r  is a pattern density at a predetermined location, 0≦d r ≦1, D(1) is an exposure dose amount having the pattern density of 100%. 
     
     
       10. The electron beam exposure method of  claim 5 , wherein the step of the calculating the exposure dose amount comprises the steps of: 
       calculating an exposure dose amount by following equation:          D        (     d   r     )       =         1   +     2                 η         1   +     2        d   r        η         ·     D        (   1   )                         
       wherein D(d r ) is the exposure dose amount, η is the backward scattering coefficient, d r  is a pattern density at a predetermined location, 0≦d r ≦1,D(1) is an exposure dose amount having the pattern density of 100%; and 
       obtaining a corrected dose amount by subtracting an increased dose amount ΔD(d r ) at the predetermined location from the exposure dose amount D(d r ).  
     
     
       11. The electron beam exposure method of  claim 10 , wherein the increased dose amount ΔD(d r ) is obtained by a variation of the backward scattering coefficient at the predetermined location of the grating region, when the backward scattering coefficient is increased from η 1  to η 2 , the increased dose amount ΔD(d r ) is obtained by following equation:          Δ                   D        (     d   r     )         =         2        (     1   -     d   r       )          (       η   2     -     η   1       )           (     1   +     2                   d   r          η   1         )          (     1   +     2                   d   r          η   2         )         ·     D        (   1   )                         
       wherein d r  is a pattern density at the predetermined location, 0≦d r ≦1, D(1) is an exposure dose amount having the pattern density of 100%. 
     
     
       12. A recording medium having stored modules with instructions executable by a computer to perform a corrected electron beam exposure, the recording medium comprising: 
       a first program module for obtaining a pattern density in one grating region produced by dividing an exposure surface into a plurality of grating regions;  
       a second program module for obtaining a backward scattering coefficient η at the one grating region in accordance with the pattern density; and  
       a third program module for obtaining an exposure dose amount from the backward scattering coefficient.  
     
     
       13. The recording medium of  claim 12 , wherein the second program module comprises a sub-program module for deciding the backward scattering coefficient η in accordance with a predetermined function in which the backward scattering coefficient η is proportional to the pattern density. 
     
     
       14. The recording medium of  claim 12 , wherein the second program module comprises a sub-program module for deciding the backward scattering coefficient η, the backward scattering coefficient η is variable in accordance with the pattern density and a location of the grating region. 
     
     
       15. The recording medium of  claim 12 , wherein the plurality of grating regions comprises a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region having a second backward scattering coefficient, the second program module comprises a sub-program module in which the second backward scattering coefficient is higher than the first backward scattering coefficient. 
     
     
       16. A recording medium having stored programs executable by a computer for performing a corrected electron beam exposure, the recording medium comprising: 
       a first program module for obtaining pattern densities of a plurality of grating regions produced by dividing an exposure region;  
       a second program module for obtaining a pattern density map with locations of the plurality of grating regions in accordance with the pattern densities;  
       a third program module for obtaining backward scattering coefficients at the plurality of grating regions in accordance with the pattern densities and the locations of the exposure region;  
       a fourth program module for generating a backward scattering coefficient map in accordance with the backward scattering coefficients; and  
       a fifth program module for obtaining a corrected exposure dose amount at one of the plurality of grating regions in accordance with the backward scattering coefficients.  
     
     
       17. The recording medium of  claim 16 , wherein the third program module comprises a sub-program module in which the backward scattering coefficients are provided with a variable function proportional to the pattern densities. 
     
     
       18. The recording medium of  claim 16 , wherein the third program module comprises a sub-program module in which the backward scattering coefficients are provided with a variable value depending on the pattern densities and the location of the grating region. 
     
     
       19. The recording medium of  claim 16 , wherein the plurality of grating regions comprises a first grating region having a patterning region having a first backward scattering coefficient and a second grating region having a surrounding region not including the patterning region and a second backward scattering coefficient, wherein the second program module comprises a sub-program module in which the first backward scattering coefficient is higher than the second backward scattering coefficient. 
     
     
       20. The recording medium of  claim 16 , wherein the fifth program module comprises a sub-program module for calculating an exposure dose amount by following equation:          D        (     d   r     )       =         1   +     2                 η         1   +     2        d   r        η         ·     D        (   1   )                         
       wherein D(d r ) is the exposure dose amount, η is the backward scattering coefficient, d r  is a pattern density at a predetermined location, 0≦d r 1, ≦D(1) is an exposure dose amount having the pattern density of 100%. 
     
     
       21. The recording medium of  claim 16 , wherein the fifth program module comprises: 
       a first sub-program module for calculating an exposure dose amount by following equation:          D        (     d   r     )       =         1   +     2                 η         1   +     2        d   r        η         ·     D        (   1   )                         
       wherein D(d r ) is the exposure dose amount, η is the backward scattering coefficient, d r  is a pattern density at a predetermined location, 0≦d r ≦1, D(1) is an exposure dose amount having the pattern density of 100%; and 
       a second sub-program module for obtaining a corrected dose amount by subtracting an increased dose amount ΔD(d r ) at a predetermined location from the exposure dose amount D(d r ).  
     
     
       22. The recording medium of  claim 21 , wherein the increased dose amount ΔD(d r ) is obtained by a variation of the backward scattering coefficient at a predetermined location of the grating region, when the backward scattering coefficient is increased from η 1  to η 2 , the increased dose amount ΔD(d r ) is obtained by following equation:          Δ                   D        (     d   r     )         =         2        (     1   -     d   r       )          (       η   2     -     η   1       )           (     1   +     2                   d   r          η   1         )          (     1   +     2                   d   r          η   2         )         ·     D        (   1   )                         
       wherein d r  is a pattern density at the predetermined location, 0≦d r ≦1, D(1) is an exposure dose amount having the pattern density of 100%.